Why do I have to use negative solidify values when the tutorial does not?
It must be because his faces normals point inwards while yours point outwards, you can check the faces orientation if you enable the Face Orientation option in the Viewport Overlay panel, the blue face means normal positive orientation, red face meaning normal negative orientation. To recalculate inside, select all in Edit mode and press ShiftCtrlN, to recalculate outside, ShiftN.